This invention relates generally to systems and methods for estimating a systematic relationship between a plurality of points, and, more particularly, to systems and methods for adaptively sampling points and estimating a form based on coordinate data and normal vector data.
The estimation of the shape of a form, such as a surface or wave, generally involves the measurement of point data associated with a plurality points on the form. For example, the point data includes a geometrical description of the location of the point on the form. The number and location of the plurality of points are generally determined by a sampling plan, which identifies the location of various sampling points whose measurements may be used to estimate the shape of the entire form. Traditionally, in order to increase the accuracy of the estimation, the number of points measured in the sampling plan are increased. Increasing the number of measured points, however, leads to a number of drawbacks. For example, each point added to the sampling plan adds cost to the estimation process by increasing the time required to measure the point and include the measurement results in the estimation. Thus, traditional sampling plans and form estimators disadvantageously require an increasing amount of time to achieve an increasing level of accuracy.
Further, for example, the points identified by the sampling plan will dramatically affect the accuracy of the estimation. Many sampling plans include a grid-like array of points having a given spaced-apart relationship. For example, such a grid-like array may be obtained in a “line scan”. In order to obtain an accurate estimation of the form, however, a sampling plan may need to include denser grids in some portions of the form, such as in portions of the form having complex shapes. Also, for example, a grid-like sampling plan having predetermined spacing may waste time making measurement in portions of the form that are uncomplicated and thus may be estimated with only a few samples. Additionally, having a sample plan that samples a lot of points in a non-complex portion of the form may increase the variability of the estimate. As such, the development of an accurate sampling plan for a given form may require a high investment in time and cost. Also, the time and cost is further multiplied for every form for which an estimate is required. Thus, the accuracy and completeness of the form estimation, as well as the time required to perform the measurements, is highly dependent on the sampling plan.
In addition, typical systems and methods for estimating a form may produce inaccurate results by including erroneous data in the estimation. For example, when measuring a form, a disturbance in the measuring system or foreign matter on the form may result in a measurement that is grossly inaccurate. Such a measurement may be referred to as an “outlier”. If such an outlier is used in estimating the form, then the estimate will not correctly represent the portion of the form adjacent to the outlier. Complex statistical models may be developed to detect and throw out such outliers, but less complex and more efficient solutions are desired.
Further, traditional systems for estimating the shape of a form typically only use the position data associated with a measured point, thereby requiring additional input to obtain accurate results. Some systems, such as line scanning systems, use surface normal data associated with a measured point to aid in guiding the probe movements to avoid interference with portions of the surface, however, this additional surface normal data is not used to estimate the shape of the form or to reduce the required number of measured points.
Therefore, systems and methods are desired to increase the efficiency, accuracy and completeness of form estimators and their associated sampling plans.